A trinomial tree method for pricing path-dependent options in a eneralized jump-diffusion model
- A trinomial tree method for pricing path-dependent options in a eneralized jump-diffusion model
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- Option contracts have become increasingly important in the field of finance
since they possess characteristics that are attractive to speculators and hedgers.
One important problem is determining the ”fair value” of an option efficiently
In this thesis, we review some basic option pricing theories. After discussing
some popular numerical methods for option pricing, we focus on dealing with
path dependent options. We first propose a generalized parabolic integro differential
equation (PIDE) model for pricing path-dependent options with jumps.
Since the PIDE model does not have a closed-form solution, in order to know
the approximate solution, we present a trinomial tree method instead of the
traditional binomial tree method and show its consistence with our proposed
PIDE model. We also give an explicit finite difference scheme and show its
equivalence to the trinomial tree scheme. Therefore we prove the uniform
convergence of the trinomial tree method for European-style path dependent
options with jumps. Further, comparison studies are performed to demonstrate
the advantages of the trinomial tree method over the binomial tree method for
pricing European put options computationally.
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